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<p>Consider</p>
<div class="displaymath process-math" data-contains-math-knowls="./knowl/eq3_25.html ./knowl/eq3_25.html">
\begin{equation}
y^{\prime \prime}+p(x) y^{\prime}+q(x) y=g(x),\tag{3.7.1}
\end{equation}
</div>
<p class="continuation">and</p>
<div class="displaymath process-math" data-contains-math-knowls="./knowl/eq3_25.html ./knowl/eq3_25.html">
\begin{equation}
y^{\prime \prime}+p(x) y^{\prime}+q(x) y=0.\tag{3.7.2}
\end{equation}
</div>
<p class="continuation">Suppose that <span class="process-math">\(y_1\)</span> and <span class="process-math">\(y_2\)</span> are a fundamental set of solutions to (<a href="" class="xref" data-knowl="./knowl/eq3_25.html" title="Equation 3.7.2">(3.7.2)</a>), i.e.,</p>
<div class="displaymath process-math" data-contains-math-knowls="./knowl/eq3_25.html ./knowl/eq3_25.html">
\begin{equation*}
y=C_1 y_1+C_2 y_2
\end{equation*}
</div>
<p class="continuation">is the general solution of (<a href="" class="xref" data-knowl="./knowl/eq3_25.html" title="Equation 3.7.2">(3.7.2)</a>).</p>
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